Hogwarts apparently has only one professor per subject. We could reason this out by looking at the fact that all of Harry's Potions classes are with Snape (for as long as Snape is teaching Potions), all of his Transfiguration classes are with McGonagall, etc., etc. Or we could observe that teachers are referred to as "the x teacher". Or we could simply look at the curse on the Defence Against the Dark Arts post.

So why is this? And how is this? There are seven years studying at Hogwarts, divided into four houses, where do they find the time to take everybody's classes? Muggle schools have entire departments dedicated to each subject, how does Hogwarts manage with only one teacher per subject? They even manage to find time to be in the staff room when some peoples' lessons are going on. For example, in The Order of the Phoenix, when Hedwig turns up injured during History of Magic, Harry rushes down to the staff room to find Prof Grubbly-Plank and comes face-to-face with Minerva McGonagall who teaches Transfiguration (a compulsory subject for the first five years) to all year groups.

All professors have time turners to attend multiple classes at the same time, just like Hermione in Prisoner of Azkaban.
– chewieSep 12 '16 at 16:47

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@AnthonyGrist Lupin needed covering once a month when he was on his wolvish period.
– user46509Sep 12 '16 at 17:33

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All my math classes in school throughout several years was (ignoring substitutes) with the same teacher even though my school had other math teachers.
– Allan S. HansenSep 14 '16 at 11:14

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Couldn't it be that there actually are several teachers to each subject, but that each teacher teaches his or her "own" students, and since Harry is the main character, we just get to see who's teaching him and his classmates?
– Duane DibbleySep 14 '16 at 11:28

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@DuaneDibbley It could, but then all of the fuss about finding someone to fill the Defence Against the Dark Arts post (compulsory subject for the first five years) doesn't make any sense, are they going through 2 or 3 DADA teachers a year? Well I think obviously not. That's really the clincher for me, but there's a lot of circumstantial evidence and I would certainly have been very interested in anything that supported the idea that actually there are more teachers we just don't see them. But I think DADA makes that idea untenable. But hey, you might convince me?
– Au101Sep 14 '16 at 11:33

7 Answers
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Out of universe, the answer is - as it usually is - that JKR is bad at maths. She likely didn't consider the kind of workload or number of lessons that would be required for there to only be a single teacher per subject.

However, let's see if we can make it work in-universe.

You stated in the question that there are seven years split between four Houses, so that gives us a starting point of 28 classes. If we assume that every year and House combination ("class") takes every subject once per week, that's 28 lessons per week.

Some subjects are taught to two Houses from the same year at once - for example, Harry and the other Gryffindors took Potions and Care of Magical Creatures with the Slytherins and Herbology with the Hufflepuffs. That may reduce the number of required lessons for some of those subjects, but not all; Potions explicitly has double periods mentioned, but I don't know if the same is true of other shared subjects, such as Care of Magical Creatures. Worst case is that it's the same amount of teaching, best case is that they save a few lessons worth of time each week.

We saw in Harry's sixth year that the number of students taking certain subjects at NEWT level was considerably lower. There only appeared to be a single sixth year class taking Slughorn's Potions class, for example. It's more likely that there's only one or two NEWT classes per subject for sixth and seventh year students. If we assume four classes (or two double periods) per year for the first five years, and only two classes per year for the last two, that brings us down to 24 lessons per week. That's probably the worst case for the core subjects.

Not all classes are taught to every year - Harry doesn't start Divination until year three - which would reduce the amount of lessons required per week by eight, so we're down to 16.

For optional classes, some subjects such as Divination seem to be (confusingly) popular, whereas others aren't. 16 lessons is our upper limit for a subject that's optional and starts in the third year, but if only one class worth of students choose to take it each year, then that drops down to only five(!!) lessons per week.

In some years, nobody opts to take a subject. I'm not sure Hagrid taught any NEWT classes to sixth years during Half-Blood Prince, for example, which would free up time in a teacher's schedule.

That assumes that each class only took a subject once per week, which isn't necessarily realistic. At least in Harry's first few years he seemed to have multiple Transfiguration and Potions lessons per week. It's possible that the later years have less classroom time due to (assumed) overall greater magical proficiency, a shorter amount of time required to practice new spells, and more theoretical study being given as homework. If we assume that each class takes every subject twice per week, rather than once, then you're looking at 48 to 56 lessons per week for a core subject (e.g. Transfiguration) and perhaps ten per week for an unpopular, optional one.

In conclusion, some Hogwarts teachers likely had very relaxed schedules (possibly teaching only ten or so lessons per week) and others had very, very busy schedules (possibly teaching as many as 56 lessons per week). If you're going to be a Hogwarts teacher you probably want to pick one of the less popular optional subjects (such as Muggle Studies) and avoid one of the core subjects like Transfiguration.

Making it worse, the core subjects also seemed to have most extra work associated with them. Snape must not only have tought 50+ lessons a week, he also demanded particularly long essays to be written by the students, was known to dismantle these very meticulously, probably needed lots of preparation for all the potions (including the management of a stock of ingredients, which of course was easy because boomslang skin is abundant and nobody needs it anyway, right?), not to speak of detentions (detention often had students “assisting” teachers, but I can't see this work too well...)
– leftaroundaboutSep 12 '16 at 20:21

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Divination is probably popular because it's easy. You can pull the answers to your homework assignments out of your nether regions and get top marks.
– TorisudaSep 13 '16 at 2:47

@leftaroundabout bet you 10 stack points that Snape had a time turner available in case of need.
– MindwinSep 13 '16 at 12:58

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JKR being bad at maths may be true, but for this question, I would suggest that the out-of-universe answer would be that she was simply trying to limit the number of characters she would have to invent.
– SimbaSep 14 '16 at 12:58

I assume JKR was modelling this on a typical British school and so I'm going to use my experience of being in one to describe a possible lesson plan for a Hogwarts teacher. We don't know exactly how many lessons everyone had and so on - this is just one possible scenario to show how it could work.

So, let's do this for one of the more "core" classes like Potions. I assume that these will be the ones with the heaviest load, student-numbers-wise, and therefore if it works for them, it should work for the others.

There seems to be two Potions classes for each year group - in Harry's year it was Griffindor and Slytherin in one class and Ravenclaw and Hufflepuff in the other. We'll call them 1A and 1B for simplicity.

At my school, we had 8 lessons a day - 4 before and 4 after lunch. Let's say in first and second year you get 4 Potions lessons a week to get up to speed in the new subject, and then from third year on you have only 2 lessons a week as you're also taking up new subjects like Divination. Let's say that continues til fifth year, and then in sixth and seventh year you go up to 4 lessons a week again as you prepare for your exams. But at exam level there will be less people taking the subjects as they are no longer compulsory, so we can merge all 4 houses into one year group.

Here's Snape's timetable for this scenario:

I've added all the classes of one "group" (e.g. 1A) next to each other for convenience; obviously in reality they would be spread out throughout the week. He's also got 4 free periods which adds a little buffer in case I've been too generous with one of my assumptions.

Here's a more realistically distributed timetable. (It assumes Snape is a Vile Morning Person™ and puts his free periods at the end of the day; this part is easily adjustable, though.)

Now, it might not be exactly like this. I've made quite a few assumptions. I don't think I've got all the details quite right about when the exams are (I'll edit later to improve this answer). But I think this example should show that it's perhaps not as wildly misguided to have one teacher per subject as other answers may suggest.

that may be good for students, but teachers have way more to do than students. you as a student have to write one essay, but your teacher has to check ALL essays. that is a lot more work. so teachers normally have less lessons than students. in your timetable the teachers have no possibilities to do their non-teaching work.
– ArminSep 14 '16 at 8:24

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@Armin: the timetable includes one free period on four days out of five. That's more than some actual teachers in actual schools get. And that's with 1st and 2nd years having 4 lessons per week - if you go with a more realistic 3 lessons per week, there could be even more free periods. (Also, at least some of the 6th and 7th year lessons could be combined, especially for potions - lab time is lab time, magic or no, and lab time doesn't depend on class year.)
– MarthaSep 14 '16 at 15:23

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@armin but the teachers don't have any commuting time as they all live in the castle, so they could do some marking before/after classes too :)
– anotherdaveSep 14 '16 at 19:16

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@anotherdave that does not matter, because normally you work 8h, regardless of whether you commute or not. same for teachers.
– ArminSep 14 '16 at 19:17

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Even out of universe, boarding schools can often have longer teaching hours, so the hours required to teach all classes doesn't need to fit into a 9am–4pm that you've expected from a day school. It's not uncommon for boarding school days to finish not much before 6pm – and that's before you start doing your marking and planning for the next day. — It's not like Hogwarts!, The Guardian 2012
– anotherdaveSep 14 '16 at 19:25

We can see from this answer What Hogwarts classes are taught to two houses at once? that there are multiple classes that are taught to at least two houses at the same time. This should make classes sized at a reasonable 20 students. This can give fairly plausible hours for each teacher(although a bit high) if we say that they teach each class 3 times a week.

2 classes per year * 7 years * teaching each class 3 times = 42 lessons.

After taking into account that some students can drop subjects it would free up some more hours for teachers. However this doesn't take into account other tasks such as correcting homework and administrative duties. However with the help of magic possibly aiding these tasks, I think it is reasonable to assume this wouldn't exceed a 40 hour working week for the average teacher. Of course, heads of houses like Snape and McGonagall may be required to work more.

Also, as a recent computer science grad, I'd be very interested in how they would organise the teachers, students and classrooms to fit this tight timetable. Magic maybe?

You can turn that into an optimization problem and let the solver of your choice solve it for you. I'm sure there's a stackexchange where you can ask how to do that if you don't already know. Of course, computers don't work in hogwarts so it's likely magic, anyway.
– SumyrdaSep 13 '16 at 18:48

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I was under the impression that "double potions" meant both two houses and double the time period. They're the "lab" classes.
– davidbakSep 15 '16 at 22:43

Because it doesn't matter - JKR didn't need to add loads of extra characters (teachers) for lessons that we'd never see. We followed Harry, Hermione and Ron who were mostly in the same lessons.

Plus it's a young adults book - no need to overly-complicate it.

Also, most books involving children at school (Jennings, Famous Five, Roald Dahl, David Walliams etc) also tend to have a single maths teacher, geography teacher etc etc, whereas the reality is that for a reasonably large school, there are usually at least 3 or 4 of each.

Indeed, from the point of view of a pupil (myself included), you only see 1 teacher for each subject.

pssst I think you may have come to the wrong place if you don't want people to overcomplicate things.
– PaulSkinnerSep 13 '16 at 10:47

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;-) Plus the OP didn't say if s/he wanted in in- our out-universe answer, but from what I remember, most books dealing with school tend to have a maths teacher, a geography teacher etc etc, whereas the reality is that for a reasonably large school, there are usually 3 or 4 of each.
– Steve IvesSep 13 '16 at 11:26

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Agreed - from a writing perspective, there's no need for lots of teachers (or other characters) that don't add interest or advance the plot in any way (I'm looking at you, Tom Bombadil). In-universe though, which is usually the approach this site prefers, there does seem to be fewer teachers than needed to run a school
– brichinsSep 13 '16 at 20:15

The simple answer is that wizards and witches are a dying breed, mostly because the bad ones are pretty effective at killing people. There aren't many wizarding families, they can only have so many children, plus mixed breeds and muggle-born wizards and witches.

There's only about five boys in Harrys year in Griffindor, so:

5 * genders * houses * years

5 * 2 * 4 * 7 = ~280 students in the whole school.

They've got round about 10 subjects, all told.

If anything, Hogwarts is MASSIVELY over-staffed.

It's only if you watch the films and see a hall full of several hundred kids that this doesn't make sense.

Hey, thanks for taking the time. 5 boys in Gryffindor, makes (we're guessing) 10 students in Gryffindor, makes (again guessing) 40 students in Harry's year (four houses), makes ~ 280 students in the whole school, which is a little more than that. Also, there's a bit of debate on the subject, but JKR has said there are roughly 600 students, roughly, and there have been suggestions that there are other characters and even other Gryffindors who we just don't see scifi.stackexchange.com/questions/59171/…
– Au101Sep 14 '16 at 11:13

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But even so, let's say there are only 280 students, it seems hogwarts takes the approach of having small class sizes. it only has two houses at a time at most (and some lessons are not explicitly shared between houses) and it never mixes years, so it doesn't really matter that the student-teacher ratio is small, the lesson-teacher ratio is still very large!
– Au101Sep 14 '16 at 11:14

Yeah, you forgot to actually multiply by the number of houses. Lower bound on the number of students is actually 4x5x2x7=280. There's probably actually more students than that: just because we only meet 5 boys in Harry's year in Griffindor doesn't mean there aren't more boys in his year.
– MarthaSep 14 '16 at 15:33

@Martha there is one Griffindor boys dormitory named in the whole series. Could Harry and Ron seriously have gone six years without ever meeting the rest of their classmates?
– AJFaradaySep 14 '16 at 15:53

@AJFaraday Well, it's not necessarily that they didn't meet them, but that we didn't meet them. I mean, supposedly Pansy Parkinson has a "gang" of Slytherin girls, but we only meet two including Pansy. However, it always seemed a bit unlikely to me that there were other Gryffindor boys, but JKR apparently once said there are about 1,000 students at Hogwarts. Slytherincess has a short discussion in this answer with a link to a slightly longer article.
– Au101Sep 14 '16 at 18:06

While the assumption that all classes are shared is not validated, this is a nice answer, short and to the point!
– TaWSep 13 '16 at 17:04

i think you misunderstood the question. the question was why binns could teach every student in hogwarts in every year and whether there was enough time for him to do that. it has nothing to do which teachers are at hogwarts. and btw, you forgot at least one teacher: arithmancy...
– ArminSep 14 '16 at 8:28

She sent an owl to Hogwarts, asking whether she might be considered for a teaching post. The owl returned within hours, offering her a job in the Transfiguration department, under Head of Department, Albus Dumbledore.

Does that mean there are official departments for at least some subjects that can include more than one person and even have somewhat complicated structure of heads and subordinates? Looks like that.

The Transfiguration Department is also mentioned in Order of the Phoenix when Ron tells Umbridge that Peeves is smashing it up. There is also mention of "Professor Sinistra of the Astronomy Department" in Chamber of Secrets and Goblet of Fire.
– AlexOct 3 '18 at 16:54